CORRECTION OF THE HEIGHT OF THE BAROMETER. 



7 • 2 2 .1.5 .7.2. 2.3 



.4.2.2.3.4.5' IT ' 2 . 2 . 3 . 2 . 2 . 3.4.2 .2.3. aVI 



2 

 and those of the last terms are — - , 



.2.2.3.4.5.6' ~ 3 ' 



2 4 2 _4_ 4 2 _4_ 4 4 



~3 ' 4 . 5' 3" '4.5' WTj' 3" ' 4T5 ' 6 . 7 ' 8 . 9 ; 



2 2 3 2 s 2 7 



— , — - — , — — , : and this series must obviously 



33. .53. .73. .9 J 



represent the sine of a circular arc, since all the other terms 



vanish in comparison with these, when b becomes infinite. 



These series however have not the convenience of afford- Inconvert'- 



ing a fluent divisible by x the absciss, as in the former case, 



and the expression for the inclination of the curve is much 



less convergent : it may however be employed where great 



accuracy is not required. Since fxyx rz n x, we find, 



y 11 



from the first equation, n x z — m xj, and 4- — — , cou- 



z m 



sequeutly — = \/(l -), and the relation of 2 and 



z mm 



b may be determined from either of the series, when n 

 and x are given. The series themselves may be thus ex- 

 panded. 



x—z +(-133333 Z s +-007 054 67 z 9 b % Expansion of 



^7 the scries. 



— {-G66667 z % + -057 1429 - + • • . 



m 



, 9n z 5 2 «> _ -000 256 533 



+ -10 — + -0108685— „ , I0 



m m* z xt b 10 — . . . 



+ -00744048 - i + ...)&* + -000 006 577 77 



13 712 _j 



+ -000 337 577 -5 —(-012 698 4 z 7 



m ' 



2" z 9 



4- -000 010 357 5 — + '014 285 7 — 

 nr m 



+ ■ • •) * 4 + . . .,) 4* 



y=(4: 



